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The solution of sparse linear systems constitutes the dominant computational bottleneck in interior point methods (IPMs), frequently consuming over 70% of the total solution time. As optimization problems scale to millions of variables,…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-05-01 Shaofeng Yang , Yunting Wang , Yingying Cheng , Fan Zhang , Xin He , Guangming Tan

In subsurface multiphase flow simulations, poor nonlinear solver performance is a significant runtime sink. The system of fully implicit mass balance equations is highly nonlinear and often difficult to solve for the nonlinear solver,…

Numerical Analysis · Mathematics 2021-11-24 Sebastian B. M. Bosma , Francois P. Hamon , Brad T. Mallison , Hamdi A. Tchelepi

This paper studies the Craig variant of the Golub-Kahan bidiagonalization algorithm as an iterative solver for linear systems with saddle point structure. Such symmetric indefinite systems in 2x2 block form arise in many applications, but…

Computational Engineering, Finance, and Science · Computer Science 2018-08-24 Mario Arioli , Carola Kruse , Ulrich Ruede , Nicolas Tardieu

Isogeometric Analysis (IgA) is a framework for setting up spline-based discretizations of partial differential equations, which has been introduced around a decade ago and has gained much attention since then. If large spline degrees are…

Numerical Analysis · Mathematics 2021-03-05 Christoph Hofer , Stefan Takacs

This paper proposes and establishes the iteration-complexity of an inexact proximal accelerated augmented Lagrangian (IPAAL) method for solving linearly constrained smooth nonconvex composite optimization problems. Each IPAAL iteration…

Optimization and Control · Mathematics 2020-06-16 Jefferson G. Melo , Renato D. C. Monteiro , Hairong Wang

This work is concerned with the convergence of the iterative solution for the Stokes flow, discretized with the weak Galerkin finite element method and preconditioned using inexact block Schur complement preconditioning. The resulting…

Numerical Analysis · Mathematics 2024-09-26 Weizhang Huang , Zhuoran Wang

Implicit methods and GPU parallelization are two distinct yet powerful strategies for accelerating high-order CFD algorithms. However, few studies have successfully integrated both approaches within high-speed flow solvers. The core…

Numerical Analysis · Mathematics 2025-09-09 Hongyu Liu , Xing Ji , Yuan Fu , Kun Xu

High-order methods gain increased attention in computational fluid dynamics. However, due to the time step restrictions arising from the semi-implicit time stepping for the incompressible case, the potential advantage of these methods…

Numerical Analysis · Mathematics 2019-10-02 Immo Huismann , Jörg Stiller , Jochen Fröhlich

This article introduces HYLU, a hybrid parallel LU factorization-based general-purpose solver designed for efficiently solving sparse linear systems (Ax=b) on multi-core shared-memory architectures. The key technical feature of HYLU is the…

Hardware Architecture · Computer Science 2026-04-02 Xiaoming Chen

In this work, we present a new scalable incomplete LU factorization framework called Javelin to be used as a preconditioner for solving sparse linear systems with iterative methods. Javelin allows for improved parallel factorization on…

Mathematical Software · Computer Science 2019-05-06 Joshua Dennis Booth , Gregory Bolet

We develop a matrix-free Full Approximation Storage (FAS) multigrid solver based on staggered finite differences and implemented on GPU in MATLAB. To enhance performance, intermediate variables are reused, and an X-shape Multi-Color…

Numerical Analysis · Mathematics 2025-10-14 Jiale Meng , Shuqi Tang , Steven M. Wise , Zhenlin Guo

Sparse linear iterative solvers are essential for many large-scale simulations. Much of the runtime of these solvers is often spent in the implicit evaluation of matrix polynomials via a sequence of sparse matrix-vector products. A variety…

Numerical Analysis · Mathematics 2026-05-12 Christie Alappat , Jonas Thies , Georg Hager , Holger Fehske , Gerhard Wellein

We present a first step towards a multigrid method for solving the min-cost flow problem. Specifically, we present a strategy that takes advantage of existing black-box fast iterative linear solvers, i.e. algebraic multigrid methods. We…

Optimization and Control · Mathematics 2016-12-02 Alessio Quaglino , Rolf Krause

We present a matrix-free GPU multigrid preconditioner with algebraically consistent coarsening for solving Poisson equations on adaptive octree grids with irregular domains. Within uniform-resolution regions, the coarsening satisfies the…

Numerical Analysis · Mathematics 2026-04-22 Mengdi Wang , Yuchen Sun , Bo Zhu

3D Gaussian Splatting (3DGS) is a recent explicit 3D representation that has achieved high-quality reconstruction and real-time rendering of complex scenes. However, the rasterization pipeline still suffers from unnecessary overhead…

Computer Vision and Pattern Recognition · Computer Science 2024-09-17 Xinzhe Wang , Ran Yi , Lizhuang Ma

The paper describes a sparse direct solver for the linear systems that arise from the discretization of an elliptic PDE on a two dimensional domain. The scheme decomposes the domain into thin subdomains, or ``slabs'' and uses a two-level…

Numerical Analysis · Mathematics 2025-09-01 Anna Yesypenko , Per-Gunnar Martinsson

We present novel improvements in the context of symbol-based multigrid procedures for solving large block structured linear systems. We study the application of an aggregation-based grid transfer operator that transforms the symbol of a…

Numerical Analysis · Mathematics 2024-03-05 Matthias Bolten , Marco Donatelli , Paola Ferrari , Isabella Furci

We present an efficient incremental SLAM back-end that achieves the accuracy of full batch optimization while substantially reducing computational cost. The proposed approach combines two complementary ideas: information-guided gating (IGG)…

Robotics · Computer Science 2026-01-14 Reza Arablouei

3D Gaussian Splatting (3DGS) based Simultaneous Localization and Mapping (SLAM) systems can largely benefit from 3DGS's state-of-the-art rendering efficiency and accuracy, but have not yet been adopted in resource-constrained edge devices…

Hardware Architecture · Computer Science 2025-10-10 Leshu Li , Jiayin Qin , Jie Peng , Zishen Wan , Huaizhi Qu , Ye Han , Pingqing Zheng , Hongsen Zhang , Yu Cao , Tianlong Chen , Yang Katie Zhao

Constructing fast samplers for unconditional diffusion and flow-matching models has received much attention recently; however, existing methods for solving inverse problems, such as super-resolution, inpainting, or deblurring, still require…

Computer Vision and Pattern Recognition · Computer Science 2024-11-04 Kushagra Pandey , Ruihan Yang , Stephan Mandt